Microeconomics
Claudia Vogel
EUV
Winter Term 2009/2010
Claudia Vogel (EUV)
Microeconomics
Winter Term 2009/2010
1 / 23
Production
Lecture Outline
Part II Producers, Consumers, and Competitive Markets
6
Production
The Technology of Production
Production with One Variable Input (Labor)
Production with Two Variable Inputs
Returns to Scale
Summary
Claudia Vogel (EUV)
Microeconomics
Winter Term 2009/2010
2 / 23
Production
Production
The theory of the rm describes how a rm makes cost-minimizing production
decisions and how the rm's resulting cost varies with its output.
The Production Decisions of a rm
The production decisions of rms are analogous to the purchsing decisions of
consumers, and can likewise be understood in three steps:
1
Production Technology
2
Cost Constraints
3
Input Choices
Claudia Vogel (EUV)
Microeconomics
Production
Winter Term 2009/2010
3 / 23
The Technology of Production
The Production Function
factors of production: Inputs into the production process (e.g., labor,
capital, and materials)
production function: Function showing the highest output that a rm can
produce for every specied combination of inputs.
q = F (K , L)
Production functions describe what is technically feasible when the rm operates
eciently.
Claudia Vogel (EUV)
Microeconomics
Winter Term 2009/2010
4 / 23
Production
The Technology of Production
The Short Run versus the Long Run
short run: Period of time in which quantities of one or more production
factors cannot be changed.
xed input: Production factor that cannot be varied.
long run: Amount of time needed to make all production inputs variable.
Claudia Vogel (EUV)
Microeconomics
Production
Winter Term 2009/2010
5 / 23
Production with One Variable Input (Labor)
Production with one Variable Input
Amount
of Labor
(L)
Amount
of Capital
(K )
Total
Output
(q )
Average
q/L)
Product(
Marginal
Product
(4q /4L)
0
10
0
-
-
1
10
10
10
10
2
10
30
15
20
3
10
60
20
30
4
10
80
20
20
5
10
95
19
15
6
10
108
18
13
7
10
112
16
4
8
10
112
14
0
9
10
108
12
- 4
10
10
100
10
- 8
Claudia Vogel (EUV)
Microeconomics
Winter Term 2009/2010
6 / 23
Production
Production with One Variable Input (Labor)
Average and Marginal Product
Output per unit of
a particular input.
average product:
Additional output
produced as an input is increased by
one unit.
marginal product:
Average product of labor = q /L
Marginal product of labor = 4q /4L
Claudia Vogel (EUV)
Microeconomics
Production
Winter Term 2009/2010
7 / 23
Production with One Variable Input (Labor)
The Law of Diminishing Marginal Returns
law of diminishing marginal returns: Principle that as the use of an input
increases with other inputs xed, the resulting additions to output will
eventually decrease.
Claudia Vogel (EUV)
Microeconomics
Winter Term 2009/2010
8 / 23
Production
Production with One Variable Input (Labor)
Example: Malthus and the Food Crisis
Claudia Vogel (EUV)
Microeconomics
Production
Winter Term 2009/2010
9 / 23
Production with One Variable Input (Labor)
Labor Productivity
labor productivity: Average product of labor for an entire industry or for the
economy as a whole.
Example: Labor Productivity and the Standard of Living
United
States
Japan
France
Germany
United
Kingdom
$82 158
$57 721
$72 949
$60 692
$65 224
Real Output per Employed Person (2006)
Years
1960-1973
1974-1982
1983-1991
1992-2000
2001-2006
Claudia Vogel (EUV)
Annual Rate of Growth of Labor Productivity (%)
2.29
0.22
1.54
1.94
1.78
7.86
2.29
2.64
1.08
1.73
4.70
1.73
1.50
1.40
1.02
Microeconomics
3.98
2.28
2.07
1.64
1.10
2.84
1.53
1.57
2.22
1.47
Winter Term 2009/2010
10 / 23
Production
Production with Two Variable Inputs
Isoquants
isoquant: Curve showing all possible combinations of inputs that yield the
same output
isoquant map: Graph combining a number of isoquants, used to describe a
production function.
Claudia Vogel (EUV)
Microeconomics
Production
Winter Term 2009/2010
11 / 23
Production with Two Variable Inputs
Substitution Among Inputs
marginal rate of technical substitution (MRTS): Amount by which the
quantity of one input can be reduced when one extra unit of another input is
used, so that output remains constant.
MRTS = − 44KL
Claudia Vogel (EUV)
Microeconomics
=
MPL )
MPK )
(
(
Winter Term 2009/2010
12 / 23
Production
Production with Two Variable Inputs
Special Cases
isoquants of perfect substitutes
Claudia Vogel (EUV)
xed-proportions production function
Microeconomics
Production
Winter Term 2009/2010
13 / 23
Production with Two Variable Inputs
Example: A Production Function for Wheat
Claudia Vogel (EUV)
Microeconomics
Winter Term 2009/2010
14 / 23
Production
Returns to Scale
Returns to Scale
returns to scale: Rate at which output increases as inputs are increased
proportionally
increasing returns to scale: Situation in which output more than doubles
when all inputs are doubled.
constant returns to scale: Situation in which output doubles when all
inputs are doubled.
decreasing returns to scale: Situation in which output less than doubles
when all inputs are doubled.
Claudia Vogel (EUV)
Microeconomics
Production
Winter Term 2009/2010
15 / 23
Winter Term 2009/2010
16 / 23
Returns to Scale
Describing Returns to Scale
Claudia Vogel (EUV)
Microeconomics
Production
Summary
Summary 1/2
A production function describes the maximum output a rm can produce for
each specied combination of inputs.
An isoquant is a curve that shows all combinations of inputs that yield a
given level of output. A rm's production function can be represented by a
series of isoquants associated with dierent levels of output.
In the short run, one or more inputs to the production process are xed. In
the long run, all inputs are potentially variable.
Production with one variable input, labor, can be usefully described in terms
of the average product of labor (which measures output per unit of labor
input), and the marginal product of labor (which measures the additional
output as labor is increased by 1 unit).
According to the law of diminishing marginal returns, when one or more
inputs are xed, a variable input is likely to have a marginal product that
eventually diminished as the level of input increases.
Claudia Vogel (EUV)
Microeconomics
Production
Winter Term 2009/2010
17 / 23
Summary
Summary 2/2
Isoquants always slope downward because the marginal product of all inputs
is positive. The shape of each isoquant can be described by the marginal rate
of technical substitution at each point of the isoquant. The marginal rate of
technical substitution of labor for capital (MRTS) is the amount by which
the input of capital can be reduced when one extra unit of labor is used so
that output remains constant.
The possibilities for substitution among inputs in the production process
range from a production function in which inputs are perfect substitutes to
one in which the proportions of inputs to be used are xed (a
xed-proportions production function).
In long-run analysis, we tend to focus on the rm's choice of its scale or size
of operation. Constant returns to scale means that doubling all inputs leads
to doubling output. Increasing returns to scale occurs when output more
than doubles when inputs are doubled; decreasing returns to scale applies
when output less than doubles.
Claudia Vogel (EUV)
Microeconomics
Winter Term 2009/2010
18 / 23
Exerxises 5
Problem 1
1
2
3
4
What is a production function? How does a long-run production function
dier from a short-run production function?
What is the dierence between a production function and an isoquant?
Isoquants can be convex, linear, or L-shaped. What does each of these
shapes tell you about the nature of the production function? What does each
of these shapes tell you about the MRTS?
Can a rm have a production function that exhibits increasing returns to
scale, constant returns to scale, and decreasing returns ro scale as output
increases? Discuss.
Claudia Vogel (EUV)
Microeconomics
Winter Term 2009/2010
19 / 23
Exerxises 5
Problem 2
Suppose a chair manufacturer is producing in the short run (with its existing plant
and equipment). The manufacturer has observed the following levels of
production corresponding to dierent numbers of workers:
1
2
3
Number of chairs
Number of workers
1
10
2
18
3
24
4
28
5
30
6
28
7
25
Calculate the marginal and average product of labor for this production
function.
Does this production function exhibit diminishing returns to labor? Explain.
Explain intuitively what might cause the marginal product of labor to become
negative.
Claudia Vogel (EUV)
Microeconomics
Winter Term 2009/2010
20 / 23
Exerxises 5
Problem 3
For each of the following examples, draw a representative isoquant. What can you
say about the marginal rate of technical substitution in each case?
1
2
3
A rm can hire only full-time employees to produce its output, or it can hire
some combination of full-time and part-time employees. For each full-time
worker let go, the rm must hire an increasing number of temporary
employees to maintain the same level of output.
A rm nds that it can always trade two units of labor for one unit of capital
and still keep output constant.
A rm requires exactly two full-time workers to operate each piece of
machinery in the factory.
Claudia Vogel (EUV)
Microeconomics
Winter Term 2009/2010
21 / 23
Exerxises 5
Problem 4
Do the following functions exhibit increasing, constant, or decreasing returns to
scale? What happens to the marginal product of each individual factor as that
factor is increased and the other factor is held constant?
1
2
3
4
5
q = 3L + 2K
q = (2L + 2K )
q = 3LK 2
q=L K
q = 4L + 4K
1
2
1
2
1
2
1
2
Claudia Vogel (EUV)
Microeconomics
Winter Term 2009/2010
22 / 23
Exerxises 5
Problem 5
The production function for the personal computers of DISK, Inc., is given by
q = 10K 0.5 L0.5 , where q is the number of computers produced per day, K is the
hours of machine time, and L is hours of labor input. DISK's competitor,
FLOPPY, Inc., is using the production function q = 10K 0.6 L0.4 .
1
2
If both companies use the same amounts of capital and labor, which will
generate more output?
Assume that capital is limited to 9 machine hours, but labor is unlimited in
supply. In which company is the marginal product of labor greater? Explain.
Claudia Vogel (EUV)
Microeconomics
Winter Term 2009/2010
23 / 23